Question

1. choose the correct graph of $y = |x - 1| + 2$.

Explanation:

Step1: Find vertex of absolute value

The vertex of $y=|x-h|+k$ is $(h,k)$. For $y=|x-1|+2$, vertex is $(1,2)$.

Step2: Test x=0 for y-value

Substitute $x=0$: $y=|0-1|+2=1+2=3$. So point $(0,3)$ is on the graph.

Step3: Test x=2 for y-value

Substitute $x=2$: $y=|2-1|+2=1+2=3$. So point $(2,3)$ is on the graph.

Step4: Match to correct graph

The graph with vertex $(1,2)$ and points $(0,3),(2,3)$ is the third option (the upward-opening V with vertex at (1,2)).

Answer:

The correct graph is the third option (the V-shaped graph with vertex at (1, 2), passing through (0, 3) and (2, 3)).